题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023517-79928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023518-73519.png)
(1)求抛物线的解析式;
(2)如图,若抛物线的顶点为P,点A关于对称轴的对称点为M,过M的直线交抛物线于另一点N(N在对称轴右边),交对称轴于F,若
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023518-59016.png)
(3)在(2)的条件下,在y轴上是否存在点G,使△BMA与△MBG相似?若存在,求点G的坐标;若不存在,请说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023518-85204.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023518-15874.jpg)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023518-67972.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023519-64091.png)
(3)点G的坐标为(0,0)或(0,-1).
解析
试题分析:(1)根据图象可得出A、B、C三点的坐标,然后用待定系数法即可求出抛物线的解析式;
(2)求出M、N点坐标,根据
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023518-59016.png)
(3)分当△AMB∽△MBG时,当△BMA∽△MBG时,两种情况讨论即可.
试题解析:(1)由题得c=1,
∵抛物线过点A(3,2)和点C
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023518-73519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023519-22660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023519-31184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023519-76936.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023520-49221.png)
∴P
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023520-58415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023520-88508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023520-66456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023521-37597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023521-33436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023521-59854.png)
过点N作
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023521-99630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023521-82007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023521-37597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023518-59016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023522-48090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023522-40280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023522-32237.png)
可求直线MN:y =" -" x+3
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023522-43753.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023522-97558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023523-25447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023523-42793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023523-28183.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023523-55277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023524-26478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023520-88508.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023524-37777.png)
当△AMB∽△MBG时,
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023524-58821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023524-96406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023525-11297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023525-17838.png)
当△BMA∽△MBG时,
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023525-81611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023525-17171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023525-75811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023526-45702.png)
综上所述,满足要求的点G的坐标为(0,0)或(0,-1).
核心考点
试题【已知抛物线经过点A(3,2),B(0,1)和点C.(1)求抛物线的解析式;(2)如图,若抛物线的顶点为P,点A关于对称轴的对称点为M,过M的直线交抛物线于另一点】;主要考察你对二次函数定义等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023512-69522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023512-11456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023512-49531.png)
A.有三个实数根 | B.有两个实数根 | C.有一个实数根 | D.无实数根 |
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023507-88318.png)
A.6 B.2
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023507-53416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023508-14642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023508-97719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023451-83319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023451-68078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023451-72489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023451-78581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023451-88277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023452-40083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023452-19488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023452-17204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023452-88286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023453-38115.png)
(1)点
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023452-17204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023453-87251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023452-17204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023453-87251.png)
(2)求顶点在直线
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023452-19488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023453-82868.png)
(3)将(2)中的抛物线沿直线
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023452-19488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023452-88286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023453-87461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023454-57219.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023454-70115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023454-37111.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019023446-17911.png)
A.k<-3 | B.k>-3 | C.k<3 | D.k>3 |
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